Contrasts or comparisons can be used to investigate specific differences between means. Contrasts, as explained by B. Thompson (1985, 1994) are coding vectors that mathematically express hypotheses. The most basic categories of contrasts are planned and unplanned. The purpose of this paper is to explain the relative advantages of using planned…

The results of a study of find alternative techniques for testing distributional normality are presented. A group of statistical techniques--some established and some new--were compared using empirical techniques. One new technique which appears to have higher power than the Lilliefors test was subjected to a better definition. Distributions under…

The Mean Cost Rating, P(A) from Signal Detection Theory, Kendall's rank correlation coefficient tau, and Goodman and Kruskal's gamma measures of predictive power are compared and shown to be different transformations of the statistic S. Gamma is generally preferred for hypothesis testing. Measures of association for ordered contingency tables are…

Post-hoc blocking and analysis of covariance (ANCOVA) both employ a concomitant variable to increase statistical power relative to the completely randomized design. It is argued that the advantages attributed to the block design are not always valid and that there are circumstances when the ANCOVA would be preferred to post-hoc blocking.…

The challenge of multiple comparisons is to maximize the power for answering specific research questions, while still maintaining control over the rate of Type I error. Several multiple comparison procedures have been suggested to meet this challenge. The stagewise protected procedure (SPP) of A. J. Klockars and G. R. Hancock tests null hypotheses…

The analysis of variance, Welch, and Brown and Forsyth tests for mean equality were compared using Monte Carlo methods. The tests' rates of Type I error and power were examined when populations were nonnormal, variances were heterogeneous, and group sizes were unequal. Recommendations for use are presented. (Author/JKS)

Contingency tables, and their associated statistical tests, are frequently used in educational and social research. Popular statistical tests used in contingency table analyses include the Pearson chi-square test and the likelihood ratio chi-square test. These two tests are chi-square distributed under large sample conditions. However, when a…

Neglected issues of simultaneous statistical inference and statistical power in survey research applications of the general linear model are reviewed, and it was found that classical hypothesis testing as it is currently applied, is inadequate for the purposes of social research. The intelligent use of statistical inference demands control over…

The literature is reviewed regarding the difference between planned contrasts, OVA and unplanned contrasts. The relationship between statistical power of a test method and Type I, Type II error rates is first explored to provide a framework for the discussion. The concepts and formulation of contrast, orthogonal and non-orthogonal contrasts are…

Five distribution-free alternatives to parametric analysis of covariance (ANCOVA) are presented and demonstrated using a specific data example. The procedures considered are those suggested by Quade (1967); Puri and Sen (1969); McSweeney and Porter (1971); Burnett and Barr (1978); and Shirley (1981). The results of simulation studies investigating…

Stability of Type I error rates and power are investigated for three forms of the Box test and two forms of the jackknife test with equal and unequal sample sizes under conditions of normality and nonnormality. The Box test is shown to be robust to violations of the assumption of normality when sampling is from leptokurtic populations. The…

Five distribution-free alternatives to parametric analysis of covariance are presented and demonstrated: Quade's distribution-free test, Puri and Sen's solution, McSweeney and Porter's rank transformation, Burnett and Barr's rank difference scores, and Shirley's general linear model solution. The results of simulation studies regarding Type I…

This study compared the model of J. E. Grizzle, C. F. Starmer, and G. G. Koch (GSK, 1969) and log-linear model-based approaches for testing hypotheses in r x c contingency tables. Tables were simulated under various conditions of table, sample, row-effect size, and column-effect size. Test statistics for column (main) and interaction effects were…

This study investigated seven methods for analyzing multivariate group differences. Bonferroni t statistics, multivariate analysis of variance (MANOVA) followed by analysis of variance (ANOVA), and five other methods were studied using Monte Carlo methods. Methods were compared with respect to (1) experimentwise error rate; (2) power; (3) number…